Re: abundance of irrationals!)

Richard Tobin wrote: 
In article <fb701d3c.0504110456.5298f0df@xxxxxxxxxxxxxxxxxx>,
W. Mueckenheim <mueckenh@xxxxxxxxxxxxxxxxx> wrote:


It talks about "ALL n" > n_0. Do you think "ALL n" supply a finite sum? 


Yes.  For all n, the sum is finite, because all for all n, n is finite.

-- Richard 

This may be incorrect or irrelevant, but I like to draw a distinction between
"for all n" and "for each n".

For example, saying "for all numbers n, there is a larger number m" could be
interpreted as meaning "there is a number m larger than any other number n".
Saying "for each number n, there is a larger number m" could not be similarly
misinterpreted, as it is clearer that the comparison is made not just once
(comparing everything to a single m), but once for each n (possibly comparing the n's to multiple m's).

Is that at all helpful in untangling the confusion?

Matt
.

Quantcast